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Disjunction elimination
In propositional calculus disjunction elimination is the inference that, if A or B is true, and both A and B entail C, then we may justifiably infer C.
For example, it's true that either I'm inside or I'm outside. It's also true that if I'm inside, I have my wallet on me. It's also true that if I'm outside, I have my wallet on me. Given these three premises, it follows that I have my wallet on me.
Formally:
( A ∨ B ) ( A → C ) ( B → C ) ∴ C
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